A representation of hyper-cubic symmetry and its projection

The symmetry elements of the four-dimensional hyper-cube are represented in a hyper-stereogram. This is used to classify the special and general directions in holosymmetric hyper-cubic symmetry. Projections of the hyper-cube in these various directions are constructed, with the incorporation of colour perspective, and the two-colour Shubnikov symmetry of these projections is tabulated and related to the four-dimensional symmetry elements on which the projection directions lie. The general representation of other four-dimensional symmetry elements in the hyper-stereogram is discussed, and the convenience of the hyper-stereogram for facilitating the evaluation of the matrices of symmetry operations in non-standard orientations is demonstrated.